Transport elements, such as tubes, cables, hoses, wires, wire bundles, and the like, are widely used in a great variety of applications. For example, a jet airliner contains approximately 3,000 custom-designed metal tubes in a number of different systems including the hydraulic system, pneumatic system, fuel system, drainage system, fire suppression system, and the like. In many of these applications, the tubes must be carefully designed in order to be manufacturable and installable. For example, the design of each tube carried by a jet airliner typically takes about 40 hours on average.
Most conventional systems, such as U.S. Pat. No. 5,227,983 to Cox, relate to the design of piping (in particular networks of piping). Such systems are concerned with automating, or helping to automate, the design of a typically approximate plan for pipes, such as in a building, ship, or factory. Piping, however, is different from the more general class of transport elements (exemplified by bent-metal tubing) that the present invention deals with, for two primary reasons. First, piping characteristically involves assembling pre-manufactured shapes (exemplified by straight sections, 90-degree elbows, 45-degree elbows, etc.) and is laid out in a generally rectilinear fashion, i.e., subsequent sections of pipes usually differ in orientation by 90 degrees or 45 degrees. In contrast, the generic class of transport elements including tubing, hoses, wires, etc. are available in, typically, straight, but sometimes also coiled, stock into which are introduced straight sections of arbitrary (or nearly arbitrary, subject to certain constraints detailed below) lengths and angles of arbitrary (or nearly arbitrary, subject to certain constraints detailed below) degrees.
Another important point of contrast is that piping layout does not generally have to be exact, but can often be approximated within an error on the order of fractions of an inch, inches, or sometimes even feet. There are two senses in which a mere approximation is tolerated: (a) failure to be precise and (b) failure to be optimal. With regard to the first sense in which a mere approximation is tolerated, failure to be precise can also be called coarseness of specification. This means that the output of the design system is not expected, or relied upon, to be correct to within a certain crude tolerance. This does not matter greatly in piping designs because a given piping design is often assembled only once, or at most a few times. This is because buildings, factories, and ships of given design are seldom manufactured in large numbers. Therefore, small errors in the design can be affordably worked-out by the persons of skill installing the pipes, such as by cutting and shaping them to the necessary dimensions in situ. In contrast, products such as airplanes and automobiles are manufactured in the thousands or even millions. Therefore, for reasons of efficiency, it is essential to have a single, exact design that can be manufactured in great numbers off-line, then moved to the point of assembly and integrated into the final product with no further modification.
With regard to the second sense in which a mere approximation is tolerated, failure to be optimal has two main aspects. First, many design domains, especially aircraft, are highly sensitive to weight and other performance measures. For example, it would typically be unacceptable for a large tube on an airliner be one inch longer than necessary, subject to the design constraints. This is because an inch of tubing, especially when filled with fluid, can weigh on the order of ounces. Thus, the thousands of tubes in an airplane, if designed with a sub-optimal system, might weight many tens, or even hundreds, of pounds more than they would had they been designed with an optimal system. Because of the harsh economics of commercial air transport, every ounce is a vital target for elimination, even on a half-million-pound vehicle. Second, each tube in an airplane is typically labored over by a human designer or team of designers for many hours. The designer manipulates the shape of the tube with a computer-aided design (CAD) system that provides an extremely detailed and realistic view of the tubes. Experienced designers possess a highly refined visual intuition about what shape they want to obtain. Simply put, they can tell when things are “off,” and they demand total and fine control in rectifying such situations. Accordingly, a conventional system suited to the design of pipes in a building is generally far too crude for designing tubes in such objects as an airplane, a jet engine, or a rocket motor. In sum, conventional systems attempt to design an approximate route or gross route, rather than refining a gross route into an precise, optimal route in the face of various constraints. The gross route is the final output of such systems. The gross route (i.e., approximate route) is in fact only the input to the present invention; the output is something optimal and perfectly manufacturable.
A tube is one type of transport element that poses a number of challenges in its design due to limitations upon the way in which the tube may be bent as described below. By way of background, tubes are generally composed of straight sections joined by circular arcs. As a result of constraints placed upon tube design by the manufacturing process, the straight sections and circular arcs each have a minimum length such that it is impossible to have an arbitrarily small bend, and one bend cannot begin an arbitrarily small distance from another bend. As shown in FIG. 1, a tube generally includes a starting point, designated the A-end, and an ending point, designated the B-end, and at least one bend defined or determined by a node, e.g., N1, therebetween. With respect to the node terminology, it is noted that for certain classes of curves, nodes are also called, e.g., control points. Since the straight segments 2 of a tube are joined by arcuate segments 4, the tube does not pass through the nodes which, instead, are imaginary points where the two adjacent straight sections would intersect if extended far enough as designated by N1 and N2 in FIG. 1. A transport element may therefore be defined in terms of its nodes supplemented by some additional information depending upon the type of transport element. In the case of a metal tube, for example, the additional information may include the radius at which the tube is bent at each bend, although typically, for the sake of efficiency, a metal tube is bent at the same radius at each bend. For other types of transport elements, such as hoses, the additional information may be, e.g., the order and knot spacings of a spline. Note that, in the context of splines, such as NURBS, what are herein called “nodes” are often called “control points,” “control polygon vertices,” or the like. “Node” is merely the prevailing term of art in the tubing business.
While nodes form a compact and intuitive representation of a tube, the use of nodes in the design of tubes may sometimes create problems. For example, a tube design may require a predetermined standoff S at the B-end, such as for tool access, as shown in FIG. 2. In this regard, standoff refers to the length of the straight segment adjacent to either the A-end or the B-end. Traditional design practice is to position the node N a sufficient distance from the B-end to provide the designated standoff. However, if the segment of the tube upstream of node N is modified as shown in FIG. 3, the standoff S′ will shrink to an unacceptable level even though the node that defined the standoff was supposedly correct. Nevertheless, even though the node does not define the standoff directly and may therefore be somewhat problematic during the design process, nodes are frequently utilized in the design of tubes because of their simplicity and intuitive appeal.
When designing the route of a transport element, such as a tube, a designer initially develops a gross route, which is an approximate description of a route, or, equivalently, a description of a set of possible routes. The gross route is typically based upon the start and end points as well as various obstacles, way-points, etc. that are located therebetween. In designing the gross route, a designer generally designs it to comply with a number of extrinsic or situation-dependent constraints that include, for example, the minimum separation from structures or other tubes, requirements that the tube be parallel to certain structures, requirements that the tube penetrate certain structures within a particular zone, etc. While termed a “route,” the gross route that is designed really defines a whole family of topologically equivalent routes that satisfy the various constraints. Based upon the gross route, a designer can select a specific route for the transport element. Unfortunately, designers cannot generally select the specific route to be optimal for a transport element and currently have no automated techniques for doing so.
Given a gross route, the specific route of a transport element is generally designed by manual drafting in a CAD system such as CATIA. This manual drafting is typically a slow and difficult process. In the case of a metal tube, it may appear that a tube centerline extending from the A-end to the B-end may be easily constructed by merely specifying some intermediate way-points at which the tube will be attached to structures at particular orientations and then having the CAD system fill in straight lines and tangential circular arcs between the A-end, the B-end and the intermediate way-points. The difficulty lies, however, in ensuring—in the face of the difficulties attached to node-based design just described—that the resulting route is manufacturable, satisfies engineering constraints and is optimal.
In the case of metal tubes, for example, the manufacturing process dictates a variety of intrinsic constraints, such as minimum bend angle, maximum bend angle, minimum straight section length between bends, constraint bend radius, etc. These constraints typically arise from the nature of tube bending machines. Generally, a tube bending machine starts with a straight piece of tubing stock and repeatedly performs various operations including shooting out a certain length of tube stock to generate a straight section, bending or wrapping the tube around a circular die to generate a circular arc, and rotating the tube about its longitudinal axis to establish a new plane for the next bend. Typically, it is expensive to change the circular die. As such, each bend in a tube preferably has the same radius. In addition, the machine must be able to grip the stock during the formation of a bend such that the bending head has a certain amount of clearance, i.e., a new bend cannot be started arbitrarily close to the previous bend. The requirement that the tube stock be gripped during bending operations therefore results in the requirement of a minimum straight section length. These constraints are termed “intrinsic” because they are defined without regard to how the tube is situated once it is installed in a machine, plant, or vehicle.
In designing the route for a tube on a CAD system, the designer essentially lays out one straight segment after another or, equivalently, defines one node after another, with the circular arcs connecting these straight sections being interpolated automatically. A variety of CAD systems are available including CATIA, Solid Edge, and Pro/ENGINEER. Typically, these systems offer the designer assistance in placing the next segment by providing an easily manipulated graphical representation of a local Cartesian coordinate system, sometimes called a “compass.” In CATIA and similar systems, the designer can place the compass anywhere in the scene, usually by using existing geometry as a base of reference. For example, if the designer wants the next section of a tube to be parallel to a particular facet of a solid, the designer can place the compass on the facet, and indicate which of its three planes is to be “paralleled.” The next tubing section is automatically constrained to lie parallel to that plane. Similar functionality is common in many graphical computer applications. The compass is essentially a way of using an inherently 2-D input device (a mouse) as an effective 3-D input device.
The compass can also be used to establish planes that cannot be penetrated during the drawing process. For example, when routing a tube near a piece of machinery from which there must be a certain amount clearance, the designer can use the compass to establish a plane defining an impenetrable barrier at the appropriate distance from the machinery. This barrier behaves like a glass wall through which the cursor cannot move.
Nevertheless, the compass, even with all the operations it provides, only supports what is still an essentially manual, sequential drafting process. As shown in FIGS. 4a-4d, the designer draws one segment of the tube, which is then frozen, and then proceeds to the next section, and so on. With respect to the sequential example provided by FIGS. 4a-4d, the tube design is frozen to the left of the dotted line. As soon as a new segment is drawn, the necessary circular arc is interpolated between the new segment and the previous segment as indicated by the dashed lines in FIGS. 4a-4d. Most CAD systems allow the designer to input minimum bend angles, minimum straight segment lengths and the like and, if the designer draws a tube segment that violates these rules, a warning is provided which may simply involve the failure to construct the tube as requested. However, conventional CAD systems do not provide the designer with any alternative suggestions for a comparable tube segment that would comply with the rules and do not consider any redesign of the previously frozen portion of the tube design. Following completion of a portion of the tube routing, the CAD system simply checks the route for compliance with various rules in a post hoc manner. For example, the CAD system may check the route to ensure that the segment just designed has a certain minimum length. (One example of the CAD system for routing transport elements that offer a mere post hoc check, albeit a rapid and interactive one, is the TubeExpert CAD program provided by Oettinger Gmbh of Oberursel, Germany.) If the post hoc check determines that one or more of the segments does not comply with the rules, the route of the transport element must be redesigned, thereby consuming a significant amount of additional time and resources.
Transport element designs are not always final. Very often it is desirable to modify an existing design. This is another area in which conventional tubing design systems are lacking. Conventional tubing design systems only support a local notion of modification, and one that never includes the automatic insertion, deletion, or re-ordering with respect to background geometry of nodes. For example, consider the tube depicted in FIG. 5. If the nodal point N4 were moved upward, a conventional CAD system would change only that portion of the route of the tube that is just next to the node that is being moved, i.e., the straight segments N3-N4 and N4-N5, and the arcs that connect these straight segments. The remainder of the tube would remain fixed. Thus, conventional CAD systems do not respond in a global way to local influences or changes—even if optimality would demand it. One way of visualizing this is to take the view in FIG. 6, that a tube is essentially a linkage of ball joints and telescoping joints. Under this view, conventional CAD systems “freeze” all the joints but the ones nearest the source of the change. For example, in FIG. 6 as N4 moves upwards, the joints or links that are circled in dashed lines in FIG. 6 are free to accommodate this movement, but the other joints or links are frozen so that the transformation of the route of the tube occurs as shown in FIG. 7. The problem with this is that the optimal (e.g., shortest) redesign is very seldom obtainable by merely local adjustments.
It is noted that the portion of the transport element that drives or originates the modification need not be a single node. For example, the designer may wish to move an entire straight segment, such as the segment between N3 and N4. If this segment were moved upward such as in response to the moving of a clamp through which this segment of the tube must pass, the route of the tube would be varied as shown in FIG. 8 in which the clamp is indicated by a rectangle. It should be noted, however, that the tube still changes shape only via the minimal, local subset of joints or links necessary to allow the upward motion of the N3-N4 segment.
As mentioned above, conventional CAD systems permit tubes to be modified automatically only in a local sense, and only if the modification does not involve the insertion, deletion, or re-ordering with respect to external constraints of nodes. The mathematical object consisting in the number of nodes and where they fall with respect to external constraints (such as hardpoints, obstacles, etc.) is called the node distribution. Put in mathematical terms, conventional CAD systems do not permit one route to be continuously deformed into another unless they have the same node distribution. Put in common CAD terms, tubes with different node distributions cannot be “rubber banded” into one another. In this regard, FIG. 9 depicts the tube extending from a fixed fitting 10 to a bulkhead 12 of an aircraft. If the position of the bulkhead 12 changed as shown in FIG. 10, the node distribution for the tube would also have to change. Crucially, FIGS. 9 and 10 illustrate that the change in the node distribution is not necessarily trivial, even in such an apparently trivial case. That is, even though it might seem that the rotation of the bulkhead could be accommodated by simply introducing one bend, it might actually require up to three bends, even for such a simple situation. (Three bends are needed if a minimum bend-angle constraint is imposed with a sufficiently large minimum bend-angle. If the angle between the bulkheads is less than this threshold, then by definition any configuration having a single bend would violate the constraint, so some number greater than one bend is needed, and in this example it is three. Minimum bend-angle constraints are pervasive in tubing design and are described below.) The key point is that, because FIG. 10 has a different node distribution from FIG. 9, the transition from FIG. 9 to FIG. 10 is not handled automatically by conventional CAD systems. The node distribution is considered inherently “part of the design”—where design means, inherently, the purview and the onus of the human designer. A conventional CAD system would require the designer to foresee the possible future rotation in FIG. 10 and build in the necessary bends into FIG. 9, where clearly they are unnecessary. In sum, the node distribution is not a one-size-fits-all aspect of a route, and even tiny changes in the constraints can impose a radically different node distribution.
The requirement that a human always design the node distribution for a route is a primary deficit of conventional tubing design systems.
By way of another example, a tube may be required to be attached to a structural element 14 as shown in FIG. 11. Most modem parametric CAD systems allow the designer to represent the clamp by associating a mathematical constraint between a point, edge or face of the structural element and an intermediate segment of the tube. Thus, if the structural element were moved downward, the route of the tube may be changed on a local basis as described above and as depicted in FIG. 12. In this regard, some CAD systems also require the designer to specify the joints and links that are free to move. For example, with respect to the route of the tube depicted in FIG. 12, in order to accommodate the downward movement of the structural element, the straight segments 16 of the tube on either side of the structural element may be elongated and the intermediate tube segment 18 may be shrunk, or the intermediate tube segment may maintain a constant length while permitting the straight tube segments on either side to stretch and all four nearby angles 20 to vary. In other words, the CAD system may not necessarily have a predefined rule or principle for determining the joints and links that are free and the joints and links that are frozen and may, instead, require input from the designer.
In contrast to the downward movement of the structural element, upward movement of the structural element can cause the route of the tube to approach an illegal configuration in which the minimum bend angle would be violated at bends 22 as shown in FIG. 13. In this regard, it is important to note that angles α are conventionally measured supplementarily as indicated in FIG. 13. While the upward movement of the structural element may be accommodated either by moving the outboard clamps downward such that the tube may assume a straight line or introducing additional nodes or bends, each of these solutions requires that the tube be (in the eyes of conventional CAD systems) “redesigned” by introducing a different number and general placement of the nodes.
Another important area of transport element CAD is multiple transport elements. Conventional CAD systems do not effectively address the potential for designing the route of a transport element based at least in part upon one or more existing or contemporaneously designed transport elements.
Further, while pre-defined path constraints, such as parameterized stay-out zones such as boxes, cylinders, and spheres, may be used to represent spatial regions or objects which a transport element should circumvent, penetrate, or pass through for routing, pre-defined path constraints may not accurately represent an object and/or may be computationally intensive to implement when attempting to approximate fine details and complicated shapes, particularly if parameterized shapes would be used for regularly-sampled distance fields. Accordingly, improved methods for designing the route of a transport element using an improved path constraint, and, in particular, an improved path constraint that accurately represents the shape of an object and is computationally feasible when designing a route for a transport element, are desired.